- #1
umby
- 50
- 8
- TL;DR Summary
- Numerical solution of a partial differential equation containing the derivative of the unknown at a point
What is the best way to solve numerically the following equation using Comsol 5.3.
##\frac{\partial T}{\partial t}=\frac{\partial ^2T}{\partial x^2}+\text{St}\left[1+\left(\frac{\partial T}{\partial x}\right)_{x=0}\right]\frac{\partial T}{\partial x}##
##T(0,t)=1##
##T(\infty ,t)=0##
##T(x,0)=\exp \left(-\frac{x^2}{\pi }\right)-x \text{erfc}\left(\frac{x}{\sqrt{\pi }}\right)##
where ##\text{St}## is a parameter which can varies from 0.01 to 100.
I am particularly interested in following the evolution of ##\text{St}\left[1+\left(\frac{\partial T}{\partial x}\right)_{x=0}\right]## with time.
Thanks in advance.
##\frac{\partial T}{\partial t}=\frac{\partial ^2T}{\partial x^2}+\text{St}\left[1+\left(\frac{\partial T}{\partial x}\right)_{x=0}\right]\frac{\partial T}{\partial x}##
##T(0,t)=1##
##T(\infty ,t)=0##
##T(x,0)=\exp \left(-\frac{x^2}{\pi }\right)-x \text{erfc}\left(\frac{x}{\sqrt{\pi }}\right)##
where ##\text{St}## is a parameter which can varies from 0.01 to 100.
I am particularly interested in following the evolution of ##\text{St}\left[1+\left(\frac{\partial T}{\partial x}\right)_{x=0}\right]## with time.
Thanks in advance.